The size distribution of galaxies in the Sloan Digital Sky Survey

We use a complete sample of about 140,000 galaxies from the Sloan Digital Sky Survey (SDSS) to study the size distribution of galaxies and its dependence on their luminosity, stellar mass, and morphological type. The large SDSS database provides statistics of unprecedented accuracy. For each type of galaxy, the size distribution at given luminosity (or stellar mass) is well described by a log-normal function, characterized by its median R̄ and dispersion σ ln R. For late-type galaxies, there is a characteristic luminosity at Mr,0 ∼ −20.5 (assuming h = 0.7) corresponding to a stellar mass M0 ∼ 10 M⊙. Galaxies more massive than M0 have R̄ ∝ M and σ ln R ∼ 0.3, while less massive galaxies have R̄ ∝ M and σ ln R ∼ 0.5. For early-type galaxies, the R̄ M relation is significantly steeper, R̄ ∝ M, but the σ ln R M relation is similar to that of late-type galaxies. Faint red galaxies have sizes quite independent of their luminosities. We use simple theoretical models to interpret these results. The observed R̄ M relation for late-type galaxies can be explained if the fraction of baryons that form stars is as predicted by the standard feedback model. Fitting the observed σ ln R M relation requires in addition that the bulge/disk mass ratio be larger in haloes of lower angular momentum and that the bulge material transfer part of its angular momentum to the disk. This can be achieved if bulge forma-